id: 06515124
dt: j
an: 2016a.00695
au: Ceauşu, Traian
ti: About the equivalence of some classical inequalities. I.
so: Gaz. Mat., Ser. B 120, No. 4, 171-179 (2015).
py: 2015
pu: Romanian Mathematical Society (Societatea de Ştiinţe Matematice din
România), Bucharest
la: EN
cc: H30 I30
ut: Cauchy inequality; root-mean-square inequality; rearrangement inequality;
Cauchy-Bunyakovski-Schwarz inequality; Bernoulli inequality; Young
inequality; Rado-Popoviciu inequality; Maclaurin inequality; Maclaurin
inequality; Rogers-Hölder inequality; Rogers inequality; Lyapunov
inequality; power-mean inequality; Minkowski inequality
ci: Zbl 0010.10703; Zbl 0987.26011; Zbl 0437.26007; Zbl 0889.26001
li:
ab: Summary: The equivalence of the classical inequalities studied in [{\it G.
H. Hardy} et al., Inequalities. Cambridge: Univ. Press (1934; Zbl
0010.10703); {\it L. Maligranda}, Math. Inequal. Appl. 1, No. 1,
69‒83 (1998; Zbl 0889.26001); ibid. 4, No. 2, 203‒207 (2001; Zbl
0987.26011); {\it A. W. Marshall} and {\it I. Olkin}, Inequalities:
theory of majorization and its applications. New York etc.: Academic
Press (1979; Zbl 0437.26007)], follows from Jensen inequality as a
property of the convex functions. Following a long way, but simple and
generally, in this paper we show that the equivalence of classical
inequalities in finite dimensional case can be proved without using
directly Jensen inequality.
rv: